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Transactions of the American Mathematical Society

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Nonlinear evolution equations and product integration in Banach spaces.


Author: G. F. Webb
Journal: Trans. Amer. Math. Soc. 148 (1970), 273-282
MSC: Primary 47.65; Secondary 34.00
DOI: https://doi.org/10.1090/S0002-9947-1970-0265992-8
MathSciNet review: 0265992
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Abstract: The method of product integration is used to obtain solutions to the nonlinear evolution equation $ g' = Ag$ where A is a function from a Banach space S to itself and g is a continuously differentiable function from $ [0,\infty )$ to S. The conditions required on A are that A is dissipative on S, the range of $ (e - \varepsilon A) = S$ for all $ \varepsilon \geqq 0$, and A is continuous on S.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0265992-8
Keywords: Nonlinear evolution equations, product integration, dissipative mapping, semigroup of nonlinear nonexpansive transformations, infinitesimal generator
Article copyright: © Copyright 1970 American Mathematical Society

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